Fast randomized algorithms for distributed edge coloring

Certain types of routing, scheduling and resource allocation problems in a distributed setting can be modeled as edge coloring problems. We present fast and simple randomized algorithms for edge coloring a graph, in the synchronous distributed point–to–point model of comput ation. Our algorithms compute an edge–coloring of a graph G with n nodes and maximum degree A with at most (1.6 + E)A + logz+d n colors with high probability (arbitrarily close to 1), for any fixed c, 6>0. To analyze the performance of our algorithms, we introduce new techniques for proving upper bounds on the tail probabilities of certain random variables. ChernoffHoeflding bounds are fundamental tools that are used very frequently in estimating tail probabilities. However, they assume stochastic independence among certain random variables, which may not always hold. Our results extend the Chernoff-Hoeffding bounds to certain types of random variables which are not stochastic ally independent. We believe that these results are of independent interest, and merit further study.